Diagramas de Flujo de Procesos Actuales

There are two ways to investigate the impact of the land rental market on income inequality: decomposition and regression. Decomposition of inequality measures can be conducted either by subgroups or by income components23. Presumably it is more convenient to decompose inequality measures by income components than by subgroups because land rental can be

23

For a formal definition of decomposability of inequality measures see Cowell (2011), pp.161-166.

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considered straightforwardly as an income generating activity for both landlord and tenant. Suppose that total income of farm household𝑖 is 𝑌𝑖(𝑖 = 1, … , 𝑁) consists of 𝐾 components 𝑌𝑖𝑗(𝑗 = 1, … , 𝐾), one of which is income from land rental activity, so that 𝑌𝑖= ∑𝐾𝑗=1𝑌𝑖𝑗.

Shorrocks (1982) and Cowell (2011) show that the coefficient of variation, variances, the Herfindahl index as well as the square of coefficient of variation can be decomposed in the same manner. These are the variance based inequality measures. Contribution of income source 𝑗 to overall inequality in the decomposition of this family of inequality indexes can be consistently represented by the variances of income source 𝑗 (or ordinal transformation of variances) plus correlations between income source 𝑗 and other income sources (or corresponding ordinal transformation of this correlation). But decomposition of the variance family indexes are rarely used in empirical studies except for the square of the coefficient of variation, or Generalized Entropy (GE) index for which the weight parameter equals 2, which satisfies the income scale independence principle (Litchfield, 1999). GE index with 𝛼 = 2 has the form

 

2

 

2

1

2

2

Y

GE

y







(5.1)

where 𝑌 = (𝑦1, … , 𝑦𝑁) is distribution of farm household income, 𝑦̅ denotes the mean income. Shorrocks (1982) has shown that,

𝜎2_{(𝑌) can be expressed as} 𝜎2_{(𝑌) = ∑ 𝜎}2_(𝑌𝑗₎ 𝐾 𝑗=1 + ∑ ∑ 𝜌𝑗𝑚𝜎(𝑌𝑗)𝜎(𝑌𝑚) 𝐾 𝑚=1 𝐾 𝑚≠𝑗

where 𝜌𝑗𝑚isthe correlation coefficient between income source 𝑗 and income source 𝑚. Substituting this result into the definition of 𝐺𝐸(2), we get 𝐺𝐸(2) =1 2 ∑𝐾 𝜎2_(𝑌𝑗₎ 𝑗=1 𝑦̅2 + 1 2 1 𝑦̅2∑ ∑ 𝜌𝑗𝑚𝜎(𝑌𝑗)𝜎(𝑌𝑚) 𝐾 𝑚=1 𝐾 𝑚≠𝑗

That is the natural decomposition noticed by Cowell and Fiorio (2011). And a natural way to represent contribution of distribution of income source 𝑗 to total income inequality is given by

 

2

 

   

2

1

2

2

K j j m jm j m j

GE

Y

Y

Y

y



 



 







_



_







(5.2) and ∑𝐾𝑗=1𝐺𝐸(2)𝑗 = 𝐺𝐸(2).

In this formulation we have 𝜌𝑗𝑚𝜎(𝑌𝑗)𝜎(𝑌𝑚) to denote correlations between different income sources. From equation (5.2) we can get income inequality caused by land rental income and interactions of land rental income with other income components. With 𝐺𝐸(2) measures on multiple periods, we can get an impression of how land rental income affects income inequality changes.

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used frequently in empirical research. Fei et al. (1978) and Lerman and Yitzhaki (1985) provide two different ways for decomposition by income sources base on different expressions of the Gini index. These decompositions, however, do not show interactions of different income components. There are also other methods of decomposition of inequality measures between income components, for example the Shapley value based decomposition proposed by Chantreuil and Trannoy (2011), which also suffers from the same problem.

It seems that if we employ different ways of decomposition we will get different measurements on the contribution of a particular income source to overall income inequality. Nevertheless if the inequality measure 𝐼(𝑌) satisfies the six assumptions stated by Shorrocks (1982) and is continuous, symmetric, and 𝐼(𝑌) = 0 if all individuals receive the same income, then the relative contribution of the income component 𝑗 to overall income inequality (or share of overall income inequality accounted by income component 𝑗) is given by





2

 

cov

j

,

/

j

s



Y Y



Y

1

. .

1

K j j

s t

s







which is indifference between inequality measures. We can show that 𝐺𝐸(2)𝑗⁄𝐺𝐸(2) = 𝑐𝑜𝑣(𝑌𝑗, 𝑌)/𝜎2(𝑌) . Therefore the decomposition of the 𝐺𝐸(2) index can produce consistent results.

Decomposition analysis can fulfill our interests on how distribution of income generated from land rental activities affects total income distribution, and how interactions of land rental income and off-farm income affects total income distribution. But in decomposition we cannot control other income sources and distributions of other income. And we cannot incorporate the land rental market imperfection. Therefore, we turn to regression analysis next.

As discussed before, land rental market imperfection and off-farm labor market imperfection became evident by means of differences between marginal return of factors and market factor prices. Furthermore, we have constructed measures for imperfect market condition. An immediate way to investigate the impact of the incomplete land and labor market on income inequality is to do regression of the inequality indexes on measurements of land and labor market imperfection, together with other explanatory variables.

Suppose that 𝐼(𝑌)_𝑣,𝑡 is measured inequality index in group (or village) 𝑣 at time 𝑡. We run the regression as follows:

𝐼(𝑌)𝑣,𝑡= 𝛼𝑣+ 𝑋𝑣,𝑡𝛽 + 𝜀𝑣,𝑡 (5.3) where 𝛼_𝑣 is group specific constant term, 𝛽 is the unknown slope parameter vector, and 𝜀_𝑣,𝑡 is the error term. 𝑋_𝑣,𝑡 is the explanatory variables vector which includes measures of land rental market imperfection and off-farm labor market imperfection (see section 4.5.1). Furthermore, we include market participation rate as

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explanatory variables. Those are proportions of farm households participating in the land rental market in village 𝑣 at time 𝑡, and proportions of labor participating in the off-farm labor market in village 𝑣 at time 𝑡.

As the data used in this study is available at household level rather than individual level, the impact of family size or economies of scale of consumption should be accounted for. Family scale economies arise when some family consumption can be shared among family members, making larger households achieve certain levels of welfare at lower per capita expenditure (Logan, 2011). This may render direct comparisons between income data from households with different sizes misleading. Thus, in income inequality measurement it is necessary to adjust household income according to family size. Rather than calculating the equivalence scale for each family member as in Pollak and Wales (1979), in this study we use the method suggested by Yin and Wan (2006). Supposed that family size is denoted by 𝑛, then the normalized family size is given by 𝑛𝛿, and adjusted household income per capita is 𝑌_𝑖∗_{= 𝑌}

𝑖⁄𝑛𝛿, where 𝛿 ∈ [0,1]. If 𝛿 = 0, then there are complete economies of scale in consumption which means everything can be shared within the family without losing utilities. 𝛿 = 1 means there is no economy of scale in consumption. In this study, we take δ as 0, 0.5, 0.8, and 1 respectively to reveal effects of economies of scale in consumption on inequality measurement. In the following analysis

we include Gini coefficient as reference.

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